In this work we present the development of the multiple sequence approximation (AGADIRms) and the standard one-sequence approximation (AGADIRls) within the framework of AGADIR's alpha-helix formation model. The extensive comparison between these new formulations and the original one [AGADIR; V. Muñoz and L. Serrano (1994). Nat. Struct. Biol., Vol. 1, pp. 399-409] indicates that the standard one-sequence approximation is virtually identical to the multiple sequence approximation, while the previously used residue partition function approximation [Muñoz and Serrano (1994); (1995), J. Mol. Biol., Vol. 245, pp. 275-296] is less precise. The calculations of the average helical content performed with AGADIR are precise for peptides of less than 30 residues and progressively diverge from the multiple sequence formulation for longer peptides. The helicity distribution of heteropolypeptides with less than 50% average helical content is also well described, while those of quasi-homopolymers with high helical content tend to be-flattened. These inaccuracies lead to an underestimation of 0.017 kcal/mol for the mean-residue enthalpic contribution in AGADIR, as compared to AGADIRms and AGADIRls. The other energy contributions to alpha-helix stability are not affected by the original statistical approximation. We also discuss the particularities of the model for alpha-helix formation utilized in AGADIR and compare it with the classical Zimm-Bragg and Lifson-Roig theories. Moreover, we develop the mathematical relationships between the basic AGADIR energy contributions and helix nucleation and elongation, which permit the quantitative comparison between formalisms. Remarkably, the comparison between AGADIRms and the Lifson-Roig formalism shows that, despite the differences on treating helix/coil cooperativity, both theories give virtually identical results when an equivalent set of parameters is used. This indicates that the helix/coil transition is a solid theory independent of the particularities of the model for alpha-helix formation.